Simple Low-Overhead Communication-Efficient String Reconciliation and Edit Distance

2026-08-19

AI Summary

本文提出了简单且通信高效的算法，用于解决长字符串相似度比较及交换问题，特别是当字符串足够相似时，通过优化通信成本和计算开销来实现。

Abstract

Suppose two parties, Alice and Bob, hold long character strings, $X$ and $Y$, respectively, and they are interested in determining how similar $X$ and $Y$ are. {Moreover, they want to exchange the strings with cost proportional to their degree of dissimilarity.} Such problems arise, for example, in database and file system synchronization operations, as well as in DNA sequence comparisons. Since the strings are long, we are interested in methods that are communication-efficient and have low overhead in terms of the computations that Alice and Bob must perform, when the strings are similar enough. In this paper, we provide simple low-overhead communication-efficient algorithms for such string reconciliation and edit distance problems. In the general case, %where the only assumption we make is that we have an upper bound, $k$, on the edit distance between $X$ and $Y$, we show how to determine the edit distance $k$ between $X$ and~$Y$ using only $O(k^2\log n)$ bits of communication and optimal $O(n)$ time overhead, with high probability. For specialized cases, such as typical English text or DNA sequences, where we can make additional well-justified assumptions about the distribution of the input strings, we show how to achieve possibly better bounds, such as $O(k\log^3 n)$ bits of communication.

Problem

• String Reconciliation
• Edit Distance
• Communication-Efficient
• Low-Overhead

Innovation

• communication-efficient
• low-overhead algorithms
• string reconciliation
• edit distance
• specialized cases